CHAPTER
10

Light – Reflection and Refraction

1. Reflection of light:
   When a ray of light incidents on a smooth polished surface and the light ray returns back in the same medium, it is called the reflection of light.
   

   In detail it can be said that if a ray of light/beam of light strikes on a polished surface, it reflects back in the same medium with certain incidence of reflection. This is a phenomenon and it is called reflection of light. The reflection of light with mirror is explained below:
   

   
   

2. Factors involves in reflection of light:
   Following factors involves in reflection of light:
   
   1. Plane polished surface from one end.
      
   2. Source of ray/light/beam of light.
      
   3. Incident ray/light.
      
   4. Resultant ray/light.
      
   5. Angle of incidence (denoted by ‘I’).
      
   6. Angle of reflection (denoted by ‘r’).
      
   7. Normal to the surface (imaginary line perpendicular to the surface).
      

   1.3    Laws of reflection: An Ancient Greek mathematician named Euclid described the law of reflection. He observed that light travels in straight lines and reflects from a smooth surface at the same angle at which it hit it.
   

       The laws of reflection is given below:
   

   1. The incident ray, the reflected ray and the normal to the surface to the mirror belong to the same plane
      
   2. The angle of incident is equal to the angle of reflection. Both angles are measured with respect to the normal to the mirror. Means to say that ‘i’= ‘r’. The same can be understand by the following diagram.
      

      
      

   2.1    Spherical mirror: Spherical mirror is a mirror which is a reflexive part of a hollow sphere. In other words, it can be said that a spherical mirror is a mirror which has the shape of a piece cut out of a spherical surface. This is explained by the following drawing:
   

   
   

   2.2    Type of Spherical mirror: From the above picture, it is seen that the surface of an sphere in the shape of a circular arc can be cut in either sides (from left and right). Hence, there are two types of spherical mirror:
   

   (a) Concave mirror:The spherical mirror whose outer
   part is painted and inner part is a reflective  surface called Concave mirror.
   
   

   (b) Convex mirror: The spherical mirror whose inner part is painted and outer part is a reflective surface called Concave mirror.

2.3    Terms relating to spherical mirror: The following common terms are necessary to discussed to learn and study about spherical mirrors:

    (a) Principal Axis: The imaginary straight line which laterally bisects an spherical mirror is called Principal Axis. Principal axis joins the Centre of curvature (C), Focus (F) and Pole (P) of the spherical mirror.

    (b) Pole: The mid-point of a spherical mirror is called pole. It is denoted by ‘P’.

  (c) Focus: The focus of a spherical mirror is a point on the principal axis of the spherical mirror at which, the light rays which are parallel to the principal axis actually converge (meet) or appear to diverge after reflection. It is denoted by ‘F’

    (d) Centre of curvature: Centre of curvature of a spherical mirror is the point which is actually the centre of the hollow sphere of which the spherical mirror belongs. It is denoted by ‘C’

    (e) Focal length: The distance between Focus to the Pole is called focal length. It is denoted by ‘f’.

    (f) Radius of curvature: The distance between centre of curvature and the Pole is called radius of curvature. It is denoted by ‘R’.

    (g) Aperture: The area of a spherical mirror which is exposed to incident light is called the aperture.

    All the above terms viz. Principal axis, Pole, Focus, Centre of curvature, Focal length, Radius of curvature & Aperture of spherical mirror is demonstrated by the following diagram:

3.1    Image formation by spherical mirror: The image formation by spherical mirrors viz. Concave mirror & Convex mirror are explained below:

3.2    Image formation by Concave mirror: The image formation by concave mirror with different positions of objects with all details are tabulated below:

    Explanation of image formation in view of the above table in the form of diagram is given below:

3.3    Uses of Concave mirror: the uses of concave mirror are as follows:

1. Concave mirrors are commonly used in torches, searchlights and headlights of vehicles to get powerful parallel beams of light.
   
2. They are used as shaving mirrors to see a larger image of the face.
   
3. Dentists use concave mirrors to view large images of the teeth of the patients.
   

3.4    Image formation by Convex mirror: The image formation by convex mirror with different positions of objects with all details are tabulated below:

Explanation of image formation in view of the above table in the form of diagram is given below:

3.5    Uses of Convex mirror: Convex mirrors always form a virtual image of the object and the image formed by the convex mirror is smaller than the size of the actual object. Therefore, the most common uses of convex mirror are in the places where bigger objects are to be viewed in a smaller size. Since convex mirrors have a wider view field than concave mirrors and plane mirrors, these are mostly used in side mirrors of automobiles. Some of the most vital and common uses of convex mirror are mentioned as follows:

• Inside buildings
  
• Sunglasses
  
• Vehicle mirrors
  
• Magnifying glass
  
• Security purposes
  

  Questions (Page – 168)
  

Q-1: Define the principal focus of a concave mirror.

Ans: Light rays that are parallel to the principal axis of a concave mirror converge at a specific point on its principal axis after reflecting from the mirror. This point is called the principal focus of the concave mirror. It is denoted by ‘F’.

Q-2: The radius of curvature of a spherical mirror is 20 cm. What is its focal length?

Ans: Radius of curvature R = 20 cm

Radius of curvature of the spherical mirror = 2 × Focal length (f) i.e. R = 2f

f= R/2 = 20 / 2 = 10 cm

Therefore, the focal length of the spherical mirror is 10 cm.

Q-3: Name the mirror that can give an erect and enlarged image of an object.

Ans: The mirror that can give an erect and enlarged image of an object is Concave Mirror.

Q-4: Why do we prefer a convex mirror as a rear-view mirror in vehicles?

Ans: Convex mirror is preferred as a rear-view mirror in cars and vehicles as it gives a wider range of view which helps the driver to see most of the traffic behind him. Convex mirrors always form an erect, virtual, and diminished image of the objects placed in front of it.

4.1    Sign convention for reflection by spherical mirrors: While dealing with the reflection of light by spherical mirrors, it is required to follow a set of sign conventions called the New Cartesian Sign Convention. In this convention, the pole (P) of the mirror is taken as the origin. The principal axis of the mirror is taken as the x-axis (x-x’) of the coordinate geometry system. The conventions complied as follows:

(a) The object is always placed to the left of the mirror. This implies that the light from the object falls on the mirror from the left-hand side.

(b) All distances parallel to the principal axis are measured from the pole (P) of the mirror.

(c) All the distances measured to the right of the origin (along +x-axis) are taken as positive while those measured to the left of the origin (along –x-axis) are taken as negative.

(d) Distances measured perpendicular to and above the principal axis (along +y-axis) are taken as positive.

(e) Distances measured perpendicular to and below the principal axis (along –y-axis) are taken as negative.

The new Cartesian sign convention is described by the following diagram:

5.1    Mirror formula and magnification: In a spherical mirror, the distance of the object from its pole is called the object distance (it is denoted by ‘u’). The distance of the image from the pole of the mirror is called the image distance (it is denoted by ‘v’). The focal length is denoted by ‘f’. There is a relationship among these three quantities (‘u’, ‘v’ & ‘f’) extracted out as mirror formula is as follows:

5.2    Derivation of Mirror formula: It is necessary to learn how the above mentioned mirror formula is derived. The derivation of the mirror formula with the help of diagram is given below.

Let an object AB is placed at a ‘u’ distance from P and it’s image formed as A₁B₁ at a distance of ‘v’.

Hence, BP = u, B1P = v & FP = f

Now, from the given diagram, it is clear that according to the law of vertically opposite angles, the opposite angles are equal. Hence, it can be written as:

The formula derived above is valid in all situations for all spherical mirrors for all positions of the object. The New Cartesian Sign Convention discussed at para 4.1 above can be used while substituting numerical values of u, v, f & R in the mirror formula for solving numerical problems.

6.1    Magnification: The term magnification refers to the process of enlarging the apparent size, not the physical size, of an object. This enlargement is quantified by a calculated number also called “magnification“. When this number is less than one, it refers to a reduction in size, sometimes called minification or de-magnification. Magnification is denoted by ‘m‘.

    If ‘h’ is the height of an object and h’ is the height of the image of the object, then the magnification ‘m’ produced by a spherical mirror is calculated as:

m = Height of the image/Height of the object.

    m = h’/h

    Here, ‘m’ is also related to the object distance (u) and image distance (v). It can be expressed as:

    m = h’/h = – v/u. Negative sign in the value of the magnification indicates that the image is           real. Positive sign in the value of the magnification indicates that the image is virtual.

    Height of the image should be taken as positive for virtual images.

Questions (Page- 171)

Q-1: Find the focal length of a convex mirror whose radius of curvature is 32 cm.

Ans: Radius of curvature R = 32 cm

Radius of curvature = 2 × Focal length (f) i.e. R = 2f

R= 2f. Hence, f = R/2 = 32/2 = 16 cm

Hence, the focal length of the given convex mirror is 16 cm.

Q-2: A concave mirror produces three times magnified (enlarged) real image of object placed at 10 cm in front of it. Where is the image located?

Ans: According to formula, the magnification produced by a spherical mirror ‘m’ is

m = (Height of the image)/(Height of the object) = – (Image distance)/(Object distance).

m = h₁/h₀ = – u/v.

Let the height of the object ho = h ,

then height of the image h1 = -3h (the image formed in real)

-3h/h = – v/u

-v/u = – 3

v/u = 3

Magnification produced by a spherical mirror:

Object distance (u)= – 10 cm

v = 3 × ( – 10) = – 30 cm

Therefore, the negative sign indicates that an inverted image is formed in front of the given concave mirror at a distance of 30 cm.

7.1    Refraction of light: The Changing of direction of light while passing from one medium to another is called refraction of light.      In other words, it can be said that when  light passes in a ‘homogeneous medium’  it’s path is straight but when the light passes  from one medium to another medium, it’s direction is changed.

7.2    Cause of Refraction: When light passes from one medium to another medium it’s velocity changes. Owing to change in velocity, it’s direction also changes. Hence, the velocity of light ray changes while passing from one medium to another and consequently refraction of light takes place.

7.3    To determine the change of light path: It the velocity in the second medium (in which the light ray enters) is less in comparison to the first medium (from which the light ray starts moving/source) then the ray bends towards the normal. Means to say that in denser medium light bends towards normal and in less dense medium, light will move away from normal. The velocity of light will decrease when the density of the medium increases.

    Example: When light enters from air (source) which is less dese medium to water (where light enters) which is denser medium, then light ray will bend towards normal. The above picture shown in para No. 7.1 is self-explanatory.

7.4    Refractive Index: The refractive index of a medium is a ratio equal to the ratio of the velocity of light in vacuum to that in the medium.

    Refractive Index of a medium = (Velocity of light in Vacuum)/(Velocity of light in that medium)

7.5    Refraction through a rectangular glass slab:
When a ray of light travels from air to class, it bends towards normal due to refraction and again when it passes through the slab and enters into air it again changes its path due to refraction.

    Example: A light ray enters into a rectangular glass slab ABCD shown in the picture diagram, it deviates with some angle ‘I’ and changes its path towards normal N₁N₂ with an angle ‘r’. The light ray might have passed in the path shown with dotted line in the diagram if no refraction takes place. Again when the refracted light ray enters into air (other medium) again refracted with an angle ‘e’ and travels away from normal M₁M₂. The dotted line shows the actual refraction (change in path of the light ray).

7.6    Laws of Refraction: (i) The incident ray, the refracted ray and the normal to the interface of two transparent media at the point of incidence, all lie in the same place. (ii) The ratio of sine of angle of incidence to the sine of angle of refraction is a constant, for the light of a given colour and for the given medium. This law is also known as ‘Snell’s law of refraction’. The value of angle lie between 0^o to 90^o (0< I < 90^o). If ‘i’ is the angle of incidence and ‘r’ is the angle of refraction, then

(Sin i)/Sin r = Constant

    The constant value is called the refractive index of the second medium with respect to the that of first.

Questions (Page – 176)

Q-1: A ray of light travelling in air enters obliquely into water. Does the light ray bends towards the normal or away from the normal? Why?

Ans: The light ray bends towards the normal. As whenever a light ray enters from an optically rarer medium (which has low refractive index) to an optically denser medium (which has a high refractive index), its speed slows down and bends towards the normal. As water is optically denser than air, a ray of light entering from air into water will bend towards the normal.

Q-2: Light enters from air to glass having refractive index 1.50. What is the speed of light in the glass? The speed of light in vacuum is 3 x 108 ms-1.

Ans: Refractive index of a medium (nm) = Speed of light in vacuum/Speed of light in the medium

Speed of light in vacuum (c) = 3 × 108 m/s

Refractive index of glass (ng) = 1.50

Speed of light in the glass (v) = Speed of light in vacuum/ Refractive index of glass

= c/ng

=3 × 108/1.50 = 2x 108 ms-1.

Q-3: Find out, from Table, the medium having highest optical density. Also find the medium with lowest optical density.

Ans: Lowest optical density = Air

Highest optical density = Diamond

The optical density of a medium is directly related with its refractive index. A medium with the highest refractive index will have the highest optical density and vice-versa.

It can be observed from the table that air and diamond respectively have the lowest and highest refractive index. Hence, air has the lowest optical density and diamond has the highest optical density.

Q-4: You are given kerosene, turpentine and water. In which of these does the light travel fastest? Use the information given in Table.

Ans: Light travel faster in water as compared to kerosene & turpentine as the refractive index of water is lower than that of kerosene and turpentine. The speed of light is inversely proportional to the refractive index.

Q-5: The refractive index of diamond is 2.42. What is the meaning of this statement?

Ans: Diamond has a refractive index of 2.42 which means that the speed of light in diamond will reduce by a factor of 2.42 as compared to its speed in the air. In other words, the speed of light in diamond is 1/2.42 times the speed of light in vacuum.

8.1    Spherical lenses: A “spherical lens” is a lens whose surface has the shape of (part of) the surface of a sphere. Convex lens.

8.2    Type of spherical lens: There are two types of spherical lens – (i) Concave lens (ii) Convex lens.

    (i) Concave lens: A concave lens is a lens which possesses at least one surface that curves inwards. It is a diverging lens, means to say that, it spreads out light rays that have been refracted through it. A concave lens is thinner at its centre than at its edges, and is used to correct short-sightedness (myopia).

(ii) Convex lens: A convex lense is a lense which is thicker (wide) at the centre and gradually decreases towards either vertical ends. Rays of light that pass through the lens are brought closer together (they converge). A convex lens is a converging lens.

8.3    Refraction by spherical lenses: Refraction by spherical lenses viz. refraction by concave lens and convex lens is called refraction by spherical lenses.

8.4    Image formation by lenses: Lenses form images by refracting light. The image formation by Concave lens and convex lens are separately discussed below:

    (a) Image formation by Concave lens: The image formation by Concave lens with respect to different position of objects are tabulated below:

8.5         Image formation by Convex lens: The image formation by Concave lens with respect to different position of objects are tabulated below:

9.1    Sign Convention for Spherical Lenses: Sign convention for spherical lenses is similar to that of spherical mirror. All rules are applied for signs of distances, except that all measurement are taken from the optical centre of the lens. According to the convention, the focal length of a convex lens is positive and that of a concave lens is negative.

9.2    Lens Formula and magnification: (a) Lens formula – The formula gives the relationship between object distance (u), image-distance (v) and the focal length (f) is the same that of spherical mirrors as discussed in para 5.1 & 5.2.

    (b) Magnification: Magnification produced by a lens is defined as the ratio of the height of the image and the height of the object. It is similar to magnification defined for spherical mirrors. Magnification is denoted by ‘m’. If ‘h’ is the height of the object and h’ is the height of the image given by a lens, then the magnification produced by the lens is –

m = h’/h

    Magnification produced by a lens is also related to the object-distance u, and image-distance v. The relationship is given by –

                     m = h’/h = v/u

10.1    Power of lens: It is already discussed that the ability of a lens to converge or diverge light rays depends on its focal length. The degree of convergence or divergence of light rays achieved by a lens is expressed in terms of its power. The power of a lens is defined as the reciprocal of it’s focal length. It is denoted by ‘P’. Hence, the power of a lens ‘P’ having focal length ‘f’ is –

P = 1/f

Questions (Page – 184)

Q-1: Define 1 dioptre of power of a lens.

Ans: Dioptre is the SI unit of power of lens is denoted by the letter D. 1 dioptre can be defined as the power of a lens of focal length 1 metre.

Q-2: A convex lens forms a real and inverted image of a needle at a distance of 50 cm from it. Where is the needle placed in front of the convex lens if the image is equal to the size of the object? Also, find the power of the lens.

Ans: The position of image should be at 2F, since the image is real and same size.

From the question, it is given that the image of the needle is formed at a distance of 50 cm from the convex lens. Therefore, the needle is placed in front of the lens at a distance of 50 cm.

Object distance (u) = – 50 cm

Image distance, (v) = 50 cm

Focal length = f

According to the lens formula,

Q-3: Find the power of a concave lens of focal length 2 m.

Ans: Focal length of concave lens f = 2 m

Power of lens P = 1/f = 1/(-2) = -0.5D

Exercise (Page – 185 to 186)

Q-1: Which one of the following materials cannot be used to make a lens?

(a) Water

(b) Glass

(c) Plastic

(d) Clay

Ans: (d) Clay cannot be used to make a lens because if the lens is made up of clay the light rays cannot pass through it

Q-2: The image formed by a concave mirror is observed to be virtual, erect and larger than the object. Where should be the position of the object?

(a) Between the principal focus and the centre of curvature

(b) At the centre of curvature

(c) Beyond the centre of curvature

(d) Between the pole of the mirror and its principal focus.

Ans: (d) The position of the object should be between the pole of the mirror and its principal focus.

Q-3: Where should an object be placed in front of a convex lens to get a real image of the size of the object?

(a) At the principal focus of the lens

(b) At twice the focal length

(c) At infinity

(d) Between the optical centre of the lens and its principal focus.

Ans: (b) The object should be placed at twice the focal length

Q-4: A spherical mirror and a thin spherical lens has a focal length of -15 cm. The mirror and the lens are likely to be

(a) both concave

(b) both convex

(c) the mirror is concave and the lens is convex

(d) the mirror is convex, but the lens is concave

Ans: (a) Both are likely to be concave.

Q-5: No matter how far you stand from a mirror, your image appears erect. The mirror is likely to be

(a) plane

(b) concave

(c) convex

(d) either plane or convex

Ans: (d) The mirrors are likely to be either plane or convex

Q-6: Which of the following lenses would you prefer to use while reading small letters found in a dictionary?

(a) A convex lens of focal length 50 cm

(b) A concave lens of focal length 50 cm

(c) A convex lens of focal length 5 cm

(d) A concave lens of focal length 5 cm

Ans: (c) A convex lens of focal length 5 cm can be used while reading small letters found in a dictionary

Q-7: We wish to obtain an erect image of an object, using a concave mirror of focal length 15 cm. What should be the range of distance of the object from the mirror? What is the nature of the image? Is the image larger or smaller than the object? Draw a ray diagram to show the image formation in this case.

Ans: Range of the distance of the object = 0 to 15 cm from the pole of the mirror.

Nature of the image = virtual, erect, and larger than the object.

Q-8: Name the type of mirror used in the following situations.

(a) Headlights of a car

(b) Side/rear-view mirror of a vehicle

(c) Solar furnace

Support your answer with reason.

Ans: (a) Concave Mirror: Because concave mirrors can produce powerful parallel beam of light when light source is placed at their principal focus.

(b) Convex Mirror: Because of its largest field of view.

(c) Concave Mirror: Because it concentrates the parallel rays of sun at principal focus.

Q-9: One-half of a convex lens is covered with a black paper. Will this lens produce a complete image of the object? Verify your answer experimentally. Explain your observations.

Ans: Yes, it will produce a complete image of the object, as shown in figure. This can be verified experimentally by observing the image of a distance object like tree on a screen, when lower half of the lens is covered with a black paper. However, the intensity or brightness of image will reduce.

Q-10: An object 5 cm in length is held 25 cm away from a converging lens of focal length 10 cm. Draw the ray diagram and find the position, size and the nature of the image formed.

Ans:

Q-11: A concave lens of focal length 15 cm forms an image 10 cm from the lens. How far is the object placed from the lens? Draw the ray diagram.

Ans: Focal length of concave lens (OF₁), f = – 15 cm

Image distance, v= – 10 cm

According to the lens formula,

The negative value of u indicates that the object is placed 30 cm in front of the lens. This is shown in the following ray diagram.

Q-12: An object is placed at a distance of 10 cm from a convex mirror of focal length 15 cm. Find the position and nature of the image.

Ans: Focal length of convex mirror (f) = +15 cm

Object distance (u) = – 10 cm

According to the mirror formula,

The image is located at a distance of 6 cm from the mirror on the other side of the mirror.

The positive and a value less than 1 of magnification indicates that the image formed is virtual and erect and diminished.

Q-13: The magnification produced by a plane mirror is +1. What does this mean?

Ans: The positive sign means image formed by a plane mirror is virtual and erect. Since the magnification is 1 it means that the size of the image is equal to the size of the object.

Q-14: An object 5 cm is placed at a distance of 20 cm in front of a convex mirror of radius of curvature 30 cm. Find the position, nature and size of the image.

Ans: Object distance (u) = – 20 cm

Object height (h) = 5 cm

Radius of curvature (R)= 30 cm

Radius of curvature = 2 × Focal length

R = 2f

f = 15 cm

According to the mirror formula,

The positive value of image height indicates that the image formed is erect.

Hence, the image formed is erect, virtual, and smaller in size.

Q-15: An object of size 7.0 cm is placed at 27 cm in front of a concave mirror of focal length 18 cm. At what distance from the mirror should a screen be placed, so that a sharp focused image can be obtained? Find the size and the nature of the image.

Ans: Object distance (u) = – 27 cm

Object height (h) = 7 cm

Focal length (f) = – 18 cm

According to the mirror formula,

The negative value of image height indicates that the image formed is inverted.

Q-16: Find the focal length of a lens of power -2.0 D. What type of lens is this?

Ans: Power of lens (P) = 1/f

P = -2D

f = -1/2 = -0.5 m

A concave lens has a negative focal length. Therefore, it is a concave lens.

Q-17: A doctor has prescribed a corrective lens of power +1.5 D. Find the focal length of the lens. Is the prescribed lens diverging or converging?

Ans: Power of lens (P)= 1/f

P = 1.5D

f = 1/1.5 = 10/15 = 0.66 m

A convex lens has a positive focal length. Therefore, it is a convex lens or a converging lens.

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